1. Field of the Invention
The present invention relates to techniques for performing oilfield operations relating to subterranean formations having reservoirs therein. More particularly, the invention relates to techniques for performing oilfield operations involving an analysis of reservoir operations, and the techniques impact on such oilfield operations.
2. Background of the Related Art
Oilfield operations, such as surveying, drilling, wireline testing, completions, simulation, planning, and oilfield analysis, are typically performed to locate and gather valuable downhole fluids. Various aspects of the oilfield and its related operations are shown in FIGS. 1A-1D. As shown in FIG. 1A, surveys are often performed using acquisition methodologies, such as seismic scanners to generate maps of underground structures. These structures are often analyzed to determine the presence of subterranean assets, such as valuable fluids or minerals. This information is used to assess the underground structures and locate the formations containing the desired subterranean assets. Data collected from the acquisition methodologies may be evaluated and analyzed to determine whether such valuable items are present, and if they are reasonably accessible.
As shown in FIG. 1B-1D, one or more wellsites may be positioned along the underground structures to gather valuable fluids from the subterranean reservoirs. The wellsites are provided with tools capable of locating and removing hydrocarbons from the subterranean reservoirs. As shown in FIG. 1B, drilling tools are typically advanced from the oil rigs and into the earth along a given path to locate the valuable downhole fluids. During the drilling operation, the drilling tool may perform downhole measurements to investigate downhole conditions. In some cases, as shown in FIG. 1C, the drilling tool is removed and a wireline tool is deployed into the wellbore to perform additional downhole testing.
After the drilling operation is complete, the well may then be prepared for production. As shown in FIG. 1D, wellbore completions equipment is deployed into the wellbore to complete the well in preparation for the production of fluid therethrough. Fluid is then drawn from downhole reservoirs, into the wellbore and flows to the surface. Production facilities are positioned at surface locations to collect the hydrocarbons from the wellsite(s). Fluid drawn from the subterranean reservoir(s) passes to the production facilities via transport mechanisms, such as tubing. Various equipment may be positioned about the oilfield to monitor oilfield parameters and/or to manipulate the oilfield operations.
During the oilfield operations, data is typically collected for analysis and/or monitoring of the oilfield operations. Such data may include, for example, subterranean formation, equipment, historical and/or other data. Data concerning the subterranean formation is collected using a variety of sources. Such formation data may be static or dynamic. Static data relates to, for example, formation structure and geological stratigraphy that define the geological structure of the subterranean formation. Dynamic data relates to, for example, fluids flowing through the geologic structures of the subterranean formation over time. Such static and/or dynamic data may be collected to learn more about the formations and the valuable assets contained therein.
Sources used to collect static data may be seismic tools, such as a seismic truck that sends compression waves into the earth as shown in FIG. 1A. These waves are measured to characterize changes in the density of the geological structure at different depths. This information may be used to generate basic structural maps of the subterranean formation. Other static measurements may be gathered using core sampling and well logging techniques. Core samples may be used to take physical specimens of the formation at various depths as shown in FIG. 1B. Well logging typically involves deployment of a downhole tool into the wellbore to collect various downhole measurements, such as density, resistivity, etc., at various depths. Such well logging may be performed using, for example, the drilling tool of FIG. 1B and/or the wireline tool of FIG. 1C. Once the well is formed and completed, fluid flows to the surface using production tubing as shown in FIG. 1D. As fluid passes to the surface, various dynamic measurements, such as fluid flow rates, pressure, and composition may be monitored. These parameters may be used to determine various characteristics of the subterranean formation.
Sensors may be positioned about the oilfield to collect data relating to various oilfield operations. For example, sensors in the drilling equipment may monitor drilling conditions, sensors in the wellbore may monitor fluid composition, sensors located along the flow path may monitor flow rates, and sensors at the processing facility may monitor fluids collected. Other sensors may be provided to monitor downhole, surface, equipment or other conditions. The monitored data is often used to make decisions at various locations of the oilfield at various times. Data collected by these sensors may be further analyzed and processed. Data may be collected and used for current or future operations. When used for future operations at the same or other locations, such data may sometimes be referred to as historical data.
The processed data may be used to predict downhole conditions, and make decisions concerning oilfield operations. Such decisions may involve well planning, well targeting, well completions, operating levels, production rates and other operations and/or conditions. Often this information is used to determine when to drill new wells, re-complete existing wells, or alter wellbore production.
Data from one or more wellbores may be analyzed to plan or predict various outcomes at a given wellbore. In some cases, the data from neighboring wellbores or wellbores with similar conditions or equipment may be used to predict how a well will perform. There are usually a large number of variables and large quantities of data to consider in analyzing oilfield operations. It is, therefore, often useful to model the behavior of the oilfield operation to determine the desired course of action. During the ongoing operations, the operating conditions may need adjustment as conditions change and new information is received.
Techniques have been developed to model the behavior of various aspects of the oilfield operations, such as geological structures, downhole reservoirs, wellbores, surface facilities as well as other portions of the oilfield operation. For example, U.S. Pat. No. 6,980,940 to Gurpinar discloses integrated reservoir optimization involving the assimilation of diverse data to optimize overall performance of a reservoir. In another example, Application No. WO2004/049216 to Ghorayeb discloses an integrated modeling solution for coupling multiple reservoir simulations and surface facility networks. Other examples of these modeling techniques are shown in Patent/Publication/Application Nos. U.S. Pat. No. 5,992,519, U.S. Pat. No. 6,018,497, U.S. Pat. No. 6,078,869, U.S. Pat. No. 6,106,561, U.S. Pat. No. 6,230,101, U.S. Pat. No. 6,313,837, U.S. Pat. No. 6,775,578, U.S. Pat. No. 7,164,990, WO1999/064896, WO2005/122001, GB2336008, US2003/0216897, US2003/0132934, US2004/0220846, US2005/0149307, US2006/0129366, US2006/0184329, US2006/0197759 and Ser. No. 10/586,283.
Reservoir simulation often requires the numerical solution of the equations that describe the physics governing the complex behaviors of multi-component, multi-phase fluid flow in natural porous media in the reservoir and other types of fluid flow elsewhere in the production system. The governing equations typically used to describe the fluid flow are based on the assumption of thermodynamic equilibrium and the principles of conservation of mass, momentum and energy, as described in Aziz, K. and Settari, A., Petroleum Reservoir Simulation, Elsevier Applied Science Publishers, London, 1979. The complexity of the physics that govern reservoir fluid flow leads to systems of coupled nonlinear partial differential equations that are not amenable to conventional analytical methods or modeling. As a result, numerical solution techniques are necessary.
A variety of mathematical models, formulations, discretization methods, and solution strategies have been developed and are associated with a grid imposed upon an area of interest in a reservoir. Detailed discussions of the problems of reservoir simulation and the equations dealing with such problems can be found, for example, in a PCT published patent application to ExxonMobil, International Publication No. WO2001/40937, and in U.S. Pat. No. 6,662,146 B1 (the “146 patent”). Reservoir simulation can be used to predict production rates from reservoirs and can be used to determine appropriate improvements, such as facility changes or drilling additional wells that can be implemented to improve production.
A grid imposed upon an area of interest in a model of a reservoir may be structured or unstructured. Such grids include cells, each cell having one or more unknown properties, but with all the cells in the grid having one common unknown variable, generally pressure. Other unknown properties may include, but are not limited to, for example, fluid properties such as water saturation or temperature, or rock properties such as permeability or porosity to name a few. A cell treated as if it has only a single unknown variable (typically pressure) is called herein a “single variable cell,” or an “IMPES cell”, while a cell with more than one unknown is called herein a “multi-variable cell” or an “implicit cell.”
The most popular approaches for solving the discrete form of the nonlinear equations are the fully implicit method (FIM) and Implicit Pressure, Explicit Saturations Systems (IMPES), as described by Peaceman, D., “Fundamentals of Reservoir Simulation”, published by Elsevier London, 1977, and Aziz, K. and Settari, A., “Petroleum Reservoir Simulation”, Elsevier Applied Science Publishers, London, 1979. There are a wide variety of specific FIM and IMPES formulations, as described by Coats, K. H., “A Note on IMPES and Some IMPES-Based Simulation Models”, SPEJ (5) No. 3, (September 2000), p. 245.
The fully implicit method (FIM) assumes that all the variables and the coefficients that depend on these variables are treated implicitly. In a FIM system, all cells have a fixed number (greater than one) of unknowns, represented herein by the letter “m.” As a result, the FIM is unconditionally stable, so that one can theoretically take any time step size. At each time step, a coupled system of nonlinear algebraic equations, where there are multiple degrees of freedom (implicit variables) per cell, must be solved. The most common method to solve these nonlinear systems of equations is the Newton-Raphson scheme, which is an iterative method where the approximate solution to the nonlinear system is obtained by an iterative process of linearization, linear system solution, and updating.
FIM simulations are computationally demanding. A linear system of equations with multiple implicit variables per cell arises at each Newton-Raphson iteration. The efficiency of a reservoir simulator depends, to a large extent, on the ability to solve these linear systems of equations in a robust and computationally efficient manner.
In an IMPES method, only one variable (typically pressure) is treated implicitly. All other variables, including but not limited to saturations and compositions, are treated explicitly. Moreover, the flow terms (transmissibilities) and the capillary pressures are also treated explicitly. For each cell, the conservation equations are combined to yield a pressure equation. These equations form a linear system of coupled equations, which can be solved for the implicit variable (typically pressure). After the pressure is obtained, the saturations and capillary pressures are updated explicitly. Explicit treatment of saturation (and also of transmissibility and capillary pressure) leads to conditional stability. That is, the maximum allowable time step depends heavily on the characteristics of the problem, such as the maximum allowable throughput, and/or saturation change, for any cell. When the time step size is not too restrictive, the IMPES method is extremely useful. This is because the linear system of equations has one implicit variable (usually pressure) per cell. In some practical settings, however, the stability restrictions associated with the IMPES method lead to impractically small time steps.
The adaptive implicit method (AIM) was developed in order to combine the large time step size of FIM with the low computational cost of IMPES. See Thomas, G. W. and Thurnau, D. H., “Reservoir Simulation Using an Adaptive Implicit Method,” SPEJ (October, 1983), p. 759 (“Thomas and Thurnau”). In an AIM system, the cells of the grid may have a variable number of unknowns. The AIM method is based on the observation that in most cases, for a particular time step, only a small fraction of the total number of cells in the simulation model requires FIM treatment, and that the simpler IMPES treatment is adequate for the vast majority of cells. In an AIM system, the reservoir simulator adaptively and automatically selects the appropriate level of implicitness for a variable (e.g., pressure and/or saturation) on a cell by cell basis (see, e.g., Thomas & Thurnau). Rigorous stability analysis can be used to balance the time-step size with the target fraction of cells having the FIM treatment (see, e.g., Coats, K. H. “IMPES Stability: Selection of Stable Time-steps”, SPEJ (June 2003), p. 181-187). AIM is conditionally stable and its time-steps can be controlled using a stability condition called the Courant-Friedrichs-Lewy (CFL) condition.
Despite the development and advancement of reservoir simulation techniques in oilfield operations, such as the FIM, IMPES, and AIM, there remains a need for a thermal adaptive implicit method (TAIM) in reservoir simulation of a thermal system with improved simulation run time and memory usage. It is desirable to calculate multiple CFL conditions in each cell concurrently. It is further desirable that such techniques for reservoir simulation be capable of one of more of the following, among others: decoupling CFL conditions in each cell for performing concurrent calculation, enabling the linear stability analysis for compositional two-phase and compositional three-phase thermal systems with inter-phase mass transfer, capillarity, and gravity effects, expanding CFL conditions from an isothermal simulator to include temperature effect for a thermal simulator, and/or estimating CFL conditions for multi-phase system with mass transfer based on CFL conditions calculated for multi-phase system without mass transfer.